How to deduce the right target for a GCC cross-build?

How to deduce the right target for a GCC cross-build?

I have a 32 bit x86 machine where Debian is up and running with this
properties
uname -r is 3.2.0-4-486 and
uname -m is i586
in this situation i have to pick the right HOST and TARGET prefix so I
will be able to cross compile gcc on another machine for this Debian
installation.
I should pick i486 or i586 ? I already tried i686 but apparently it
doesn't work at all ( gcc compiles and runs, it's the gcc/g++ compiler
that doesn't find the headers on the machine using the i686 prefix ).